• Our book The Joy of Set about the card game SET has been published! My co-authors are Liz McMahon and our daughters Rebecca and Hannah. The game is a model for 4-dimensional affine space over the finite field of size 3. Here's a nice review.
• The other math book I co-authored is Matroids: A Geometric Introduction, co-authored with Prof. Jennifer McNulty of U. Montana. This is a gentle introduction to matroid theory. Please send comments, corrections, and compliments. Here is a Lafayette-produced blurb that talks about me and the book.
• I am the Problem Editor for Math Horizons (see below).

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Brief Bio:

I'm from Miami and I'm a lifelong Dolphins fan, both the mammals and the NFL version. I got my BA from the University of Florida in 1977 and my Ph.D. from the University of North Carolina in 1983.  My mathematical interests include combinatorics, geometry and algebra.  I love baseball, mostly as a spectator.  I like rock climbing and biking, and so do my wife and mathematical teammate, Liz McMahon, and my two daughters, Rebecca and Hannah.  Here are a few family pictures that are pretty old.


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Math Horizons

I am the current Problem Editor for Math Horizons. Please send me your solutions to current problems, but also your own problems for consideration. Here's a sample:


Problem 290 (April, 2013): I have an ordinary deck of 52 cards, and I am playing a game of solitaire as follows: First, starting with a nicely shuffled deck, I lay out 8 cards, face up. Then I remove any four of the cards if their sum is a multiple of 4 (counting J=11, Q=12 and K=13). After removing those four cards, I replace them with four new cards, and I continue this process.

Here's the problem: Is it possible for me to get stuck at any point along the way? Or is it true that I will always be able to clear the deck, regardless of the initial order of the 52 cards in the deck? [Answer below]

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Mathematics Competitions

I'm involved in the following math competitions: 

• LVAIC Mathematics Competition
• Weekly Barge Competition
• Putnam Exam
• Math Bowl

Problems sometimes lead to sequences: One problem I published awhile ago (American Math Monthly - Problem 11218, solved in the April, 2008 issue) forms the basis for a sequence in the on-line integer sequence catalog. Two more sequences came out of the Facet Derangements paper I wrote with Liz.

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Publications

Here is a list of published and current work. I've worked on matroids (representability questions), greedoids (extending the Tutte polynomial from graphs and matroids to greedoids), graph invariants & reliabilty, and geometric questions related to matroids (comparing matroid automorphism groups to Coxeter groups). Some reliability programs of Dave Eisenstat are available here and here, but I have no idea if these links still work. From 2000-2010, I was Lafayette's REU contact; but the correct person to contact now is Liz McMahon or Derek Smith. 

As a sample of what my writing has degenerated into, here's an April Fool's article published by Math Horizons in 2007.

Finally, if you're interested in the card game SET, our book is out. Hannah won the first national SET competition; she is the First SET Grand Master.


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Teaching

I've taught a variety of math courses and one non-math course. The math courses include Calculus, Numerical Analysis, Linear Algebra, Abstract Algebra, Real Analysis, Combinatorics, Matroid Theory, Graph Theory, Symmetry & Geometry, Discrete Structures, Operations Research and Statistics.  The non-math courses include a first year seminar on The Science of Polling, and a course on Intelligence Testing and other controversies in science. I also taught a Matroid Theory course in Argentina as part of a Fulbright grant in 2015. For some geometric fun, check out inversion in a circle and Euler line & center of nine-point circle constructions in Cinderella. You can also play with the Toricelli point of a triangle. I've directed several senior theses in combinatorics, geometry and game theory and independent studies on a variety of topics.


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Hillel Society

I'm a co-advisor (with Liz McMahon) for Lafayette's very active Hillel Society. History professor Bob Weiner is the Jewish Chaplain at Lafayette, and my colleague Ethan Berkove is the official Hillel advisor. We have Shabbat dinners every Friday night - stop by at 6:00.  


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Horizon Problem Solution

You can always clear the deck. Any eight integers must contain a subset of size four that sums to a multiple of 4, and, since the entire deck sums to a multiple of 4, the last 4 cards must be a multiple of 4, too.

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Topology of tire tracks in New Zealand